Find the exponential model that best fits the graph's points. Exponent should be rounded to four decimal places.

Question

Find the exponential model that best fits the graph&#039;s points. Exponent should be rounded to four decimal places.

Liyana Mansell · Accepted Answer

Given points on the exponential model: (0,1) and (5,16).  General equation of an exponential model: y=aebx  Evaluate the general equation at x=0 and x=5:  y=aeb(0)=ae0=a(1)=a  y=aeb(5)=ae5b  We require y=1 when x=0 and y=16 when x=5 (as the points (0,1) and (5,16) need to lie on the exponential model).  a=1  ae5b=16  By the first equation, we thus know that a=1. Let us replace ae5b=16 by 1 in the second equation:  e5b=16  Take the natural logarithm from each side of the previous equation (also using that the natural logarithm is the inverse of the exponential).  5b=ln⁡16  Let us use the power property of logarithms (lna^b=blna) along with 16=24:  5b=4ln⁡2  Divide each side of the previous equation by 5:  b=4ln⁡25  Replacing a by 1 and b by 4ln⁡25 in the general equation of the exponential model, we then obtain:  y=e4ln⁡25x

Find the exponential model that fits the points shown in the graph. (Round the exponent to four decimal places)

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